SOME INVERSE EIGENPROBLEMS FOR JACOBI AND ARROW MATRICES

We consider the problem of reconstructing Jacobi matrices and real sym metric arrow matrices from two eigenpairs. Algorithms for solving thes e inverse problems are presented. We show that there are reasonable co nditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with litt le or no cancellation. The algorithm is particularly elegant for the t ridiagonal matrix associated with a bidiagonal singular value decompos ition.